To address your point about Batman killing, then we will have to dig a little deep into the dream sequence before the flash appears...
The dream or to be more exact,a point in distant future,where superman has gone rogue because Lois has been killed is an indication that the DCEU is following the Injustice storyline.
The soldiers who are killed by Batman by gunfire are enhanced by abilities given to them by a pill which the Man of Steel has created to resurrect an army of his own.
So even if Batman is shown shooting at them point blank,they wont be killed as they are enhanced.
But since Zack would want to bring his own taste to the mix of DCEU, the flying creatures in the sequence suggest that Superman has either knowingly or out of choice has created an alliance with DARKSEID.
Now this is new as their is no such allegiance in the comicsverse.
Now coming back to the point where Batman has to kill the Russian to save Martha is an indication or rather a tribute to the comics where in some dream of Superman after the death of Lois, batman kills Joker, his nemesis,to save Lois and therefore prevents Superman from going rogue...
P.S:Do correct me if i missed something :)